The effect of intraparticle convection on nutrient transport in porous biological pellets

Abstract Intraparticle convection has been neglected in the majority of reaction—diffusion studies in porous catalysts to date. However, this transport mode can contribute significantly to the total intraparticle transport rate, especially in the case of reactants of limited solubility, such as oxygen, frequently encountered in biotechnological applications. In this work, a regular perturbation method is employed for the derivation of the flow field inside a porous particle subject to external free fluid flow conditions. It is shown that the intrapellet and extrapellet Peclet numbers are generally related by a linear scaling relationship, Pein ≈ e Peout where e, is a small number proportional to the hydraulic permeability of the particle and inversely proportional to the square of the characteristic length. External transport is further studied and found to be unaffected by intraparticle fluid flow. Following the above findings, the intrapellet diffusion—convection—reaction problem is formulated and solved analytically for a zeroth-order nutrient uptake rate. From the obtained solution a general condition is derived between the Peclet number and Thiele modulus for the prevention of nutrient depletion everywhere in the pellet. This condition is proposed as a fundamental criterion for the design of porous pellets and optimal operation of processes involving biological catalysts.